A fluid can generally be classified as ideal, Newtonian or non-Newtonian based on the behavior of the fluid under stress. An ideal fluid has no shear stress in a flow field and its viscosity is zero. No fluids which exhibit this type of behavior exist. In a Newtonian fluid, such as water and glycerol, the shear stress is directly proportional to the shear rate; and its viscosity is independent of the shear rate. In a non-Newtonian fluid, the shear stress is dependent on the shear rate and its viscosity may vary with the shear rate in a complex manner.
Viscosity is a measurement of the behavior of a fluid under stress. It is therefore, important to be able to accurately determine the viscosity of a fluid in order to improve the design of pumps, stirrers, mixers, liquid transport devices, and reactors. Furthermore, the molecular weight of a polymer solution is related to its viscosity at zero shear rate and an accurate determination of the zero shear rate viscosity of a polymer solution enables one to obtain an accurate measurement of its molecular weight.
Density of a fluid is defined as its mass per unit volume. In certain instances it is desirable to determine the density of a fluid along with its viscosity under identical conditions. Density and viscosity vary with temperature and it would be desirable to determine both over a wide temperature range.
Many methods have been developed to determine the viscosity of fluids. The earliest is the capillary type viscometer in which a fluid flow is provided through a capillary tube and the drop in pressure across a length of the tube is used to determine the viscosity. This technique suffers from many disadvantages. It is difficult to accurately measure the small pressure differences involved, precisely calibrate the diameter of the capillary tube and keep the capillary tube clean. Further, the capillary tube viscometer is only applicable for determining the viscosity at high shear rates. It cannot be used to determine viscosity at low shear rates.
Another technique is the falling sphere or falling ball viscometry first described in G. G. Stokes, Camb. Phil. Trans., 9, p. 8 (1851). In this method the viscosity is determined from the time taken for a sphere to fall through a predetermined distance in an infinite fluid. However, in the falling sphere method, the following assumptions are made: the spheres are falling in an infinite medium, the density of the falling sphere is in a suitable range for the equation used to determine the viscosity to hold true, and the sphere must be perfectly round, so that it will fall vertically through the fluid and will not veer in one direction or another or fall erratically.
In practice, spheres can only be made from a limited range of materials, such as, glass, aluminum or steel and the density cannot be adjusted. Further, very few spheres are truly round and, as a consequence, the fall through the fluid medium is often not vertical. Moreover, a fluid must be held in a container, therefore, wall effects have to be considered. Thus, inaccuracies arise from the non-vertical fall of a sphere and a correction factor for wall effects must be applied. Moreover, the falling sphere method does not provide an exact solution for non-Newtonian fluids because of the geometric complexities involved.
Falling cylinder and falling plunger viscometers have also been designed. See, Lohrentz, et al., A. I. Ch. E. Journal, 6, No. 4, p. 547-549 (1960) and G. S. Smith, J. Inst. Pet., 43, p. 227-230 (1957). These are found wanting because it is difficult to construct the falling cylinder or plunger, difficult to obtain cylinders or plungers with different densities and difficult to maintain a vertical fall through the fluid. To maintain a vertical fall through the fluid, guide pins or bushings are required. Further, the eccentricity effect is very significant. Because of these problems, it is difficult to account for the systematic error in viscosity measurement by the falling cylinder or plunger method.
A rotating cylinder viscometer with two coaxial cylinders, a rotating outside cylinder and a stationary inside cylinder, has been developed to measure the viscosity of non-Newtonian fluids. See Van Wazer et al., Viscosity and Flow Measurement, p. 47-96, Interscience Publishers, New York, 1963. However, the rotating cylinder viscometer is difficult and expensive to make because small torque measurements on the stationary spindle are needed for compensation purposes. Further, it is very difficult to maintain a constant temperature in the system and evaporation of the fluid from the open mouth container is unavoidable. These difficulties often translate into unacceptably large errors in the viscosity obtained.
Recently, an apparatus and method for the accurate determination of the viscosity of Newtonian and non-Newtonian fluids which is simple and easy to use has been developed. That apparatus is the subject of U.S. patent application Ser. No. 697,747 filed Jan. 24, 1985, now U.S. Pat. No. 4,637,250 entitled Apparatus and Method For Viscosity Measurements For Newtonian and Non-Newtonian Fluids by the present inventors, which patent is incorporated herein by reference as if set forth in full. The apparatus includes a cylinder for holding the fluid for which the viscosity is to be determined, a needle, a funnel placed at the top of the cylinder for feeding the needle into the fluid in the cylinder, means at the bottom of the cylinder for collecting the needle, means for maintaining the cylinder and its contents at a constant temperature, and means for measuring the time of fall of the needle between two marks on the wall of the cylinder space a predetermined distance. The needle is made of tubing of a material selected from glass, aluminum or stainless steel and is capable of being adjusted in density with thin metal inserts and sealed hemispherically at both ends. The viscosity is measured by allowing the needle to fall through the liquid in the cylinder while maintaining the cylinder and its contents at a constant temperature. The time of fall of the needle between the two spaced marks on the cylinder or transducers is measured. From this measurement and the dimensions of the apparatus, the viscosity can be calculated.
For many purposes, it is also desirable to know the density of the liquid as well as its viscosity. Standard techniques for measuring density are not good for high temperature liquids since it is not possible to heat the apparatus used to measure the density to these high temperatures. Therefore, it would be desirable to be able to determine the density of the fluid, particularly at substantially the same time and with the same apparatus used to measure the viscosity of the liquid.